I'm with you on the "for the people" point. But remember that franchises and timetables, many fares and (increasingly) the finer details of rolling stock allocation, etc, are all specified and commissioned by the DfT. That is already public.
In terms of "by the people" I'm completely non-dogmatic. If the public sector can do it best, fine. If you can shunt risk to a private sector provider for a reasonable sum, that's fine too.
We can argue about the latter point, but it is important to be clear that we have an outsourced / franchised railway, not a private railway. A true private railway would be owned and run by the private sector and it would run such services at such prices as it felt would be most profitable. That is a long way from where we are now.
I agree that we don't have a truly 'private' railway. We could never have such a thing without most of the network shutting. If there is a profitable core to the passenger network, it's very small.
I have a problem with the 'privatised' system for the following reasons:
(1) The claim (repeated today in the press and by Grayling) that privatisation has somehow transformed the railway from the 'bad old days'. There is no justification for this view. Perhaps the introduction of cheap advanced fares, but it's hard to believe a nationalised rail industry would not have done something similar. All improvements in the past 20 years are down to the massive increase in government spending, not private sector 'magic'.
(2) The current structure has too much reliance on the DfT, which should set policy and funding (the two need to be compatible of course); implementation and organisation should be left to the rail industry.
(3) Franchising doesn't seem to have achieved anything other than create artificial constraints on the industry. Things that need doing don't get done because it's too much hassle to change the franchise agreement, and you only get major improvements agree once every 8-10 years.
(4) What should be an integrated organisation is split into myriad companies creating unnecessary complexity. It kind of works on a normal day but when things go wrong or major changes are needed (electrification projects, timetable changes) it falls apart. These projects are complicated but they should be bread and butter for a railway in a modern country.